A “universal” model of metastatic cancer, its parametric forms and their identification: what can be learned from site-specific volumes of metastases

Abstract

We develop a methodology for estimating unobservable characteristics of the individual natural history of metastatic cancer from the volume of the primary tumor and site-specific volumes of metastases measured before, or shortly after, the start of treatment. In particular, we address the question as to what information about natural history of cancer can and cannot be gained from this type of data. Estimation of the natural history of cancer is based on parameterization of a very general mathematical model of cancer progression accounting for primary tumor growth, shedding of metastases, their selection, latency and growth in a given secondary site. This parameterization assumes Gompertz (and, as a limiting case, exponential) growth of the primary tumor, exponential growth of metastases, and exponential distribution of metastasis latency times. We find identifiable parameters of this model and give a rigorous proof of their identifiability. As an illustration, we analyze a clinical case of renal cancer patient who developed 55 lung metastases whose volumes were measured through laborious reading of CT images. The model with maximum likelihood parameters provided an excellent fit to this data. We uncovered many aspects of this patient's cancer natural history and showed that, according to the model, onset of metastasis occurred long before primary tumor became clinically detectable.

A Stochastic Model for Cancer Metastasis: Branching Stochastic Process with Settlement

“…Our approach to model the shedding time and other random times (introduced below) by exponential distributions is motivated by the memoryless property, which characterizes the exponential distribution: assuming that the tumor is big enough, cell clusters are shed randomly approximately at a constant rate, which implies an exponential distribution for the shedding time. Moreover, our assumption of exponentially distributed times between events (shedding and establishment) is supported biologically by the successful confrontation of Hanin et al's stochastic model to clinical data (Hanin et al, 2016).…”

Artificial Intelligence and Mechanistic Modeling for Clinical Decision Making in Oncology

“…140 Growth suppression by the primary tumorsubsequently leading to postsurgery acceleration-was also mathematically inferred in another study by Hanin et al analyzing data of 55 lung metastases from a patient with kidney cancer. 141 Metastatic appearance and growth has also been studied through the lens of clonal evolution. 136 In such models, each cell has, per time unit, a probability to mutate and acquire metastatic ability, and then a probability to leave the primary tumor and establish a distant metastatic colony.…”

Implications of Immune-Mediated Metastatic Growth on Metastatic Dormancy, Blow-Up, Early Detection, and Treatment

“…In this section, we assume that the dynamics of the tumor are slow relative to those of the immune system. This assumption is biologically reasonable, as immune dynamics -such as immune response to an injury -occur on the timescale of minutes or hours [42], whereas tumor dynamics, especially dormant metastases, can be on the timescale of years or even decades [24]. Under the assumption of two timescales, we will perform quasi-steady state analysis of the model (1) using methods from geometric singular perturbation theory [25,27].…”